The Lanczos Potential for Bianchi Spacetime

TL;DR

This paper investigates the Lanczos potential in Bianchi spacetimes, deriving differential equations and exploring their solutions to understand gravitational energy in cosmological models.

Contribution

It provides a detailed analysis of the Lanczos potential in Bianchi spacetimes and formulates differential equations relevant for cosmic energetics.

Findings

Derived coupled first-order PDEs for the Lanczos potential

Solved these equations for specific Bianchi configurations

Applied results to study gravitational energy in the universe

Abstract

The form and application of the Lanczos potential for Bianchi spacetime are studied. The Lanczos potential is found in some specific cases then the general case studied. It leads to two coupled first order partial differential equations which although they so far have not been solved in general can be solved for many configurations. The application is to cosmic energetics: in other words to the study of the energy of the gravitational and other fields in the Universe.